Computes the randomized response estimation, its variance estimation and its confidence interval through the Mangat-Singh-Singh model (Mangat el al., 1992) when the proportion of people bearing the innocuous attribute is unknown. The function can also return the transformed variable. The Mangat-Singh-Singh-UB model can be seen in Chauduri (2011, page 54).
MangatSinghSinghUB(I,J,p1,p2,pi,type=c("total","mean"),cl,N=NULL,pij=NULL)first vector of the observed variable; its length is equal to \(n\) (the sample size)
second vector of the observed variable; its length is equal to \(n\) (the sample size)
proportion of marked cards with the sensitive attribute in the first box
proportion of marked cards with the sensitive attribute in the second box
vector of the first-order inclusion probabilities
the estimator type: total or mean
confidence level
size of the population. By default it is NULL
matrix of the second-order inclusion probabilities. By default it is NULL
Point and confidence estimates of the sensitive characteristics using the Mangat-Singh-Singh-UB model. The transformed variable is also reported, if required.
A person labelled \(i\) who is chosen, is instructed to say "yes" if he/she bears \(A\), and if not, to randomly take a card from a box containing cards marked \(A,B\) in proportions \(p_1\) and \((1-p_1),(0<p_1<1)\); they are then told to report the value \(x_i\) if a \(B\)-type card is chosen and he/she bears \(B\); otherwise he/she is told to report "No". This entire exercise is to be repeated independently with the second box with \(A\) and \(B\)-marked cards in proportions \(p_2\) and \((1-p_2),(0<p_2<1,p_2\neq p_1)\). Let \(I_i\) the first response and \(J_i\) the second response for the respondent \(i\).
The transformed variable is \(r_i=\frac{(1-p_2)I_i-(1-p_1)J_i}{p_1-p_2}\) and the estimated variance is \(\widehat{V}_R(r_i)=r_i(r_i-1)\).
Chaudhuri, A. (2011). Randomized response and indirect questioning techniques in surveys. Boca Raton: Chapman and Hall, CRC Press.
Mangat, N.S., Singh, R., Singh, S. (1992). An improved unrelated question randomized response strategy. Calcutta Statistical Association Bulletin, 42, 277-281.
# NOT RUN {
N=802
data(MangatSinghSinghUBData)
dat=with(MangatSinghSinghUBData,data.frame(I,J,Pi))
p1=0.6
p2=0.8
cl=0.95
MangatSinghSinghUB(dat$I,dat$J,p1,p2,dat$Pi,"mean",cl,N)
# }
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